AbstractContext. On October 24, 2007 the periodic comet 17P/Holmes underwent an astonishing outburst that increased its apparent total brightness from magnitude
up to
in roughly two days. In this contribution we report on Wendelstein 0.8 m telescope (WST) photometric observations of the early evolution stages of the outburst. Aims. We studied the evolution of the structure morphology and its kinematic and provide an estimate of the ejected dust mass. Methods. We analyzed 126 images of the comet in the BVRI photometric bands spread between October 26, 2007 and November 20, 2007. The bright comet core appeared to be separated from a quickly expanding dust cloud in all the data, and the bulk of the cloud was contained in the field of view of our instrument during the days soon after the outburst, allowing precise estimates both of the separation velocities of the two luminous baricenters and of the expansion velocity of the dust cloud. The ejected dust mass was derived on the basis of differential photometry on background stars occulted by the moving cloud. Results. The two cores were moving apart from each other at a relative, projected constant velocity of
arcsec/day (
km s-1). In the inner regions of the dust cloud we observed a linear increase in size at a mean constant velocity of
arcsec/day (
km s-1). Evidence of a radial velocity gradient in the expanding cloud was also found. Our estimate for the expanding coma's mass was approximately
10-2-1 comet's mass, implying a significant disintegration event. Conclusions. We interpret our observations in the context of an explosive scenario that was more probably triggered by some internal instability processes rather than by an impact with an asteroidal body. Due to the peculiar characteristics of this event, further observations and investigations are necessary to bring the nature of the physical processes that determined it to light.

1 Introduction

In this Letter, we concentrate on analyzing the outburst
of comet 17P/Holmes which occurred on October 24, 2007
(Santana 2007). We provide an overview analysis of the early evolution
phases of the surrounding cometary environment in the period between
October 26 and November 20, 2007 considering
the global structure of the expanding material and its kinematic properties
and inferring the ejected dust mass. Comet brightenings are well-documented
in the literature, and in general they may be associated
with evident cometary nuclear fragmentation (see e.g. Sekanina
et al. 2002, and references therein). Despite their recurrence,
the magnitude and the characteristics of the outbursts on comet
17P/Holmes largely justify its longstanding
reputation in the annals of astronomy (Barnard 1896).

The periodic comet 17P/Holmes was discovered on
November 6, 1892 by
E. Holmes in London, during an outstanding brightness increase,
followed by another similar event on January 16, 1893.
When discovered by Mr. Holmes, the comet
was around 5 months past perihelion
(T = June 13).
On October 24, 2007, around 6 months after the last perihelion passage (T = May 4, 2007), the comet
underwent a phenomenon similar to
those observed more than one hundred years
ago. The heliocentric distance of
the object at the time of the two major
events was around
= 2.39 AU in 1892 and
= 2.44 AU in 2007,
and the orbital inclination remained
substantially unaltered during this
period (
).
This Letter is structured in the following way. In
Sect. 2, we present the observations
and the data reduction method. In Sect. 3,
we discuss the morphological evolution of the expanding
structure. In Sect. 4, we calculate the separation
velocities between the comet and the center of the dust cloud,
as well as the expansion velocity of the cloud.
In Sect. 5, we estimate the ejected dust mass.
Finally in Sect. 6, we sum up our results.

2 Observations and reduction of the data

The observations were acquired on
October 26/28/29/31, 2007 and November 2/5/20, 2007. A total number
of 126 images were analyzed in the BVRI filters, and an
overview of the observations is shown in
Table 1.
The images
were acquired using the MONICA CCD camera, at the Cassegrain
focus of the 0.8 m Wendelstein telescope, with a scale
of 0.5 arcsec/pix and a field of view of around
arcmin.
The pre-reduction was done using standard reduction software
(MUPIPE) specifically developed at the Munich Observatory for the
MONICA CCD camera (Gössl & Riffeser 2002).
The weather conditions were in general clear for all our observing
nights with the exception of night 26,
which was cloudy. Otherwise we were able to
acquire 1 image in the R band that night and to use it
for analyzing
the kinematic properties of the cloud described in
Sect. 4. The exposure times varied between
40 and 200 s for the whole dataset.

Table 1:
Number of images of 17P/Holmes taken during
the different observing nights in the
BVRI filters.

During night 28, the photometric conditions were both good and stable
over the whole night, and we thus acquired some images of the
Landolt standard field PG0918
in all our filters.
We obtained 2 images in the B, V, R bands and 4 images in the I band.
These data were
reduced in exactly the same manner as the scientific
observations (see also Sect. 5). The magnitudes
of the standard stars were reported to 1 airmass
and 1 arcsec and finally calibrated to the Landolt
photometric system, thanks to the Stetson Photometric
Standard Fields
data of PG0918. We found a total of 26 common stars
between our catalog and the one provided by Stetson,
and obtained the following calibration equation for the R band
against the V-R color:

The
residual of the fit with
respect to the best-fitting least-square linear model was 0.02 mag.
This result gives an idea of our photometric precision
during that night, and it will be useful in Sect. 5 in the
discussion of the ejected mass estimate.

3 The evolution of the morphological structure

To show the evolution of the morphological structure of
the object, we selected one
representative image in the R band for each night in our
dataset. These images were
scaled to the same exposure time, airmass, and intensity range,
in order to properly sample the surface brightness of the coma in the whole
dataset. The lowest intensity level was chosen close to the lowest
counts we got on the last image of our
dataset, while the highest was chosen close to
the coma's peak intensity of the image taken on October 28, 2007.
We did not process the image acquired on October 26, 2007 in this way,
because it was too noisy.
The images were then normalized to the lowest intensity level. Finally, we
displayed the images codified on a logarithmic
color scale, as shown in Fig. 1. We overplotted
the isophote intensities levels to each panel
to highlight the structure of the inner
part of the cloud.

The most interesting
feature in Fig. 1 is the presence of two bright
cores (the comet core being towards the upper left side).
These two cores were increasingly
separating during the observing period and appeared
elongated towards each other, indicating an exchange
of mass. Moreover, the expansion of the global structure
is evident from the sequence of images. We also displayed the intensity value of the closest
isophote to the cloud's center and of the adjacent one in the
outwards direction. The exact values given by the isophotes depend on the adopted number of
isophotes in each panel, which also determines the intensity step between
them. We set the number of isophotes to approximately provide
the same sampling of the inner regions of the cloud. Thus, the quoted
numbers must be considered as indicative of the relative
surface brightnesses of the cloud on the different nights. The intensity
of the innermost isophote of night 2007 Oct. 28 was around 2 orders of
magnitude larger with respect to the correpondent isophote's intensity of night
2007 Nov. 20, and the intensity step between the isophotes was also 1order of magnitude larger in the first case with respect to the second.
We emphasize that
there is no way to significantly change these conclusions by adopting different
isophotal mapping criteria, as we accurately verified.
Actually, both these results are the consequence of the rapid expansion
of the dust cloud, which determines a steady decrease in its surface
brightness, and a more homogeneous light distribution in the more
evolved and less concentrated phases.

Figure 1:
Snapshot of R band images acquired during each night of our
observing run, showing the evolution of
comet 17P/Holmes' morphological structure.
Each image has been scaled to the
same exposure time, airmass, and intensity range
and
displayed on a logarithmic color scale, codified by the bottom
color bar. The top 6 images are zoomed inside the inner
regions of the object and have a field of view of
arcmin, whereas
the last one arcmin.
Two cores are visible in all the images, the comet
nucleus (on the upper left side) and the core of
the coma, rapidly separating
during the observing period.
The values reported for the
coma's innermost isophotes of each
panel (or in the close-up views of 28/29/31 nights) show
the surface brightness decrement of the coma due
to its rapid expansion.

4 Kinematic of the expanding materials

In this section we derive the separation velocity of the two bright
baricenters and the dust cloud's expansion velocity. The
comet's center appeared in all our images as a point-like source, so
the peak's position was derived with a Gaussian fitting algorithm,
as for stellar objects. The light distribution of the dust cloud was
extended over a much larger area and was not Gaussian overall, but we found
that the inner part could be always represented by a Gaussian.
We thus fit a bidimensional
Gaussian using the light distributions along the x and y axis. An initial
guess for the centroid was provided with a maximum finding algorithm run
in a small region around the peak (30 arcsec). Then a least-square
fit provided the refined position for the centroid
and the
and
of the
fitting Gaussians. In Fig. 2 (left panel)
we plotted the two bright cores' projected distances against the Julian date
(JD) of the observations. The correction for the Earth's
variable distance has been taken into account, although it is negligible.
We obtained a uniform increasing separation with a mean velocity of
arcsec/day (
km s-1).
The uncertainties are dominated by the errors in the diffuse
cloud centroids. In the right panel of Fig. 2,
we report the
of the diffuse clouds (actually the mean of the
and )
as a function of the JD.
We did not include the last two nights in this figure,
because the cloud was too expanded.
Two images acquired on night 2007 Nov. 2 in the R band were also excluded because
of the large offset of the cloud's centroid with respect to the
image's center. The errorbars in this figure were calculated as the
difference of the
along the x and y axes.
The different colors in the figure codify observations
obtained in the different photometric bands. Also in this case
we observed a linear increase in size with a mean velocity of
arcsec/day (
km s-1). Repeating
the calculation separately for the different
bands gave the results in Table 2.
These mean values and their errors
were obtained using a weighted least-square algorithm.
The different bands allow exploration of the different layers of the expanding
cloud, more external in the B and deeper in the redder
bands. Thus, this result can be interpreted as evidence of a
radial velocity gradient in the expanding cloud. For each couple of
adiacent bands, we considered the ratio between the
difference of the expansion velocities reported in Table 2
and the difference in the correspondent
values given by the
least-square fitting
models for the night 2007 Nov. 2, for which we obtained the largest separation among
the expanding shells. Taking the mean of these values, we obtained an estimate
of the radial velocity gradient during that night equal to
,
which means an increase of
around 0.3 cm/s every km going from the center to the surface of
the coma.

Figure 2: Left: angular projected distance between the
centroid of the two bright baricenters, for all the images in our
dataset, against the
of
the observations. The continuous line denotes the best fit linear
model. On the left hand y-axis values are in arcsec, whereas
on the right hand y-axis values are in km.
Right:
of the expanding cloud
Gaussian core against .
Different colors indicate
measurements obtained in different bands: B in black, V in
blue, R in red and I in yellow. The best fit linear
models in each band are represented by the continuous lines.

All these kinematic observations could be explained in the
context of an explosive scenario. While, as a consequence of the explosion,
a part of the cometary nucleus was disintegrated and the material was
outflowed in all directions resulting in the sperically symmetric expanding
coma, and the survived nucleus received a kick separating from the coma's
center with the observed projected velocity. The expansion velocity
of a particle of radius a during an explosive event is proportional
to a-1 (see e.g. the discussion in Tozzi et al. 2007)
implying a higher expansion velocity for the smaller,
less massive particles than for the
larger and more massive ones,
which resulted in the observed velocity
gradient in the expanding cloud.

The formation of spherical expanding envelopes around the cometary
nucleus of 17P/Holmes was observed for both the events
in November 1892 and January 1893.
Bobrovnikoff (1943) compared the observations
by different authors between 16 and 22 January 1893,
deriving a uniform expansion velocity of
km s-1,
similar to what we found here.
The sudden brightness variations, the formation of
spherical dust envelopes with similar kinematic properties, the
correspondence in the orbital phase at the instant of the major outbursts
noted in Sect. 1, point towards a common mechanism
at the base of the observed phenomena. Moreover, the distance from the
ecliptic plane was around 0.8 AU in both cases.
Given that, although it cannot be completely excluded,
it seems unlikely that
the above-mentioned explosive mechanism was triggered by an asteroidal impact,
making it more probably an internal instability process.

Table 2:
The derived expansion velocities in arcsec/day along with their
uncertainties for the expanding dust cloud in the different bands.
In parenthesis we report the corresponding values in km s-1.

5 The ejected mass estimate

In the following we provide an estimate of the ejected dust mass during the
outburst, through the extinction produced by the dust cloud on the
surrounding background stars. We selected two well-exposed,
seeing images taken on October 28, 2007 in the R filter.
These images had the largest time
separation (2 h) in the whole dataset, among equal filter images
acquired during the same observing night.
Thus, they provided the largest apparent
motion of the cloud on the sky plane. At the same time, this
temporal difference is small enough to avoid the expansion of the
cloud changing the extinction map significantly,
thereby allowing a homogeneous comparison
of the two images. Finally, day 28 was close
enough to the outburst to allow the dust cloud to fit well inside our field of
view.
We performed PSF fitting photometry with
DAOPHOT/ALLSTAR (Stetson 1987) and rejected
all the stars with
and
any absolute sharp values bigger than 1.
These parameters and selection criteria allowed those objects to be excluded
for which
a reliable fit of the stellar model could not be performed, because close
to saturation, or close to bad pixels, and to reject non-stellar sources
such as cosmic rays, background galaxies, or
spikes of saturated stars.
The sky background in these images was estimated locally around each star
in an annular region comprised 1.5 and 3.5 arcsec from the stars'
centroids. This region was selected after performing different tests looking
for the best subtraction of the analyzed stars. The modal value of the pixel
counts inside the selected annular region was considered as the estimate of
the sky background. The photometry was extracted in a circular
region centered on the stars' centroids with radius equal to 1.3 arcsec, which
corresponded to the seeing value in both images. The derived magnitudes
were then reported to 1 airmass and 1 s of exposure time for both the
images. We then considered all the common
objects with a radial distance from the center of the comet
>25 arcsec and with radial distance from the center
of the cloud <3 arcmin in both the images.
The inner limit was needed to avoid the
photometry of the stars being biased by the luminous core of the comet. The
outer limit was chosen to avoid detector border effects,
accounting for the position of the center of the cloud in both the images.
At the end, we obtained a catalog of
20 stars spread inside the analyzed region of the cloud;
see Fig. 3.

Figure 3: Top: spatial distribution of the 20 background stars
used in Sect. 5 to probe the differential
extinction produced by the coma, for the two images acquired on
October 28, 2007. The image on the left was taken 2 h before
the right one.
The selected stars are
indicated by white circles. The associated numeration
corresponds to the one in the lower panel,
allowing each star to be related to the correspondent
measured differential extinction.
Bright sources were saturated
(black regions), as well as was the center of the cometary nucleus.
The black lines indicate the distances, referred to in
Sect. 5 as r1 and r2, of
one star with respect to the
estimated coma's centers.
Bottom: the correlation between the differential extinctions in
the R band ()
and the x parameter
(see text for details).

To demonstrate the radial dependence of the
extinction from the center of the cloud,
we assumed a uniform and homogeneous,
spherically symmetric mass distribution.
Thus, because r is the position
of one star with respect to the cloud's center,
we can express the optical depth of
the cloud at the distance r as

(1)

where
is the length
of the segment of sphere with projected
distance r with respect to the cloud's center, Ris the radius of the cloud,
the cross section of
the dust grains in a given observing band, and n the number density
of the dust particles. Considering two different positions r1 and
r2 of a generic star in the first and second images
with respect the cloud's center,
we can express the differential extinction
produced by the
cloud in the two positions as

(2)

which implies

=

=

(3)

where m1, I1 and m2, I2 are the observed
magnitudes (intensities) of the star at positions r1 and r2,
respectively. As easily recognized, this model satisfies
the required symmetry conditions with respect
to r1 and r2. Actually, if
r1 is equal to r2, the differential extinction should be zero.
Morever, if we consider two stars with initial r1,
and final r2,
positions,
which satisfy the condition
and
,
the resulting
differential extinctions for the
two stars should be equal and opposite in sign.
In particular,
should
be positive when r1<r2 (the star is moving away from the cloud center,
and thus is less extincted in r2with respect to r1), and negative
when r1>r2 (the star is going towards the
cloud center). This implies that
the angular coefficient
in Eq. (3) should be positive.
The value of
gives the extinction
for unitary length in the given observing band.
Therefore, we fit to the observed differential extinctions the model

(4)

where
,
and the
coefficient was included to account for
residual constant zero points between the two images.
The result, after subtracting the
constant zero point, is shown in the bottom panel of
Fig. 3. We found a positive
correlation between the differential extinction ,
and the x parameter, as expected. The derived
value of the
coefficient was
mag/pix, where a pixel
corresponds to around 592 km
at the distance of the comet. This value has
been obtained assuming a radius R for the cloud of 3 arcmin
(
for that night for the luminous distribution
analyzed in Sect. 4). Increasing the radius to 4 arcmin
()
implies a value of
mag/pix.

The most important assumptions of the model
are the dust cloud's spherical geometry and the homogeneous and uniform
mass distribution. The geometry of the
cloud was well-constrained by the observations
and the analysis presented in the previous
sections. As for the second hypothesis, it
allowed expression of the optical depth in a straightforward and
convenient way, as shown in Eq. (1), and
ultimately implies the linear dependence
of the observed differential extinctions on the geometrical
factor x. A strong deviation from that assumption
would imply a strong deviation from the linear model prediction,
which is not observed (Fig. 3).
The scatter in that relation
(0.06 mag) is greater than
the scatter derived from the calibration of
the Landolt standard field discussed in Sect. 2 (0.02 mag).
Otherwise, in the science
images, the surface brightness of the coma determined a background around 10 times larger than in the Landolt images, which explains the factor of 3 increase in the scatter.
The radial velocity gradient of the expanding material
discussed in Sect. 4 points away from the uniform mass
distribution hypothesis. Otherwise, as
shown in the right panel of Fig. 2, during
night 28 the expanding shells were certainly more concentrated
than in the later evolved phases
since closer that night to the outburst.
In conclusion, it is reasonable to believe that, on the chosen night, the
material was not far from being uniformly distributed and homogeneously mixed,
and we considered this hypothesis as a good
approximation of the structural properties of the observed coma.
Therefore, the dominant factor that explains the observations is related to
the cloud's geometrical structure, in the sense that the observed differential
extinctions were determined by the variable quantity of mass over the cloud's
different line of sights probed by the background stars (directly implied by its
spherical structure). This is demonstrated overall by the observed linear dependence
of the differential extinction on the geometrical factor x and by the
positive value of the
coefficient, also predicted by the model.

To derive the coma's mass, we considered
spherical dust grains with a mean density
(
)
and a ``typical'' dimension (and thus mass
).
Thanks to the definition of the
parameter in Eq. (3),
the mass of the cloud M can be expressed through the
formula

M

=

=

(5)

where the grain's cross-section
was taken equal to the geometrical cross-section
and the numerical factor is 2.6.
We varied the
value of
inside a range of characteristic grain dimensions,
m (Mathis et al. 1977), and the dimension of the
cloud R between 3-4 arcmin.
The derived estimate for the coma's mass was between
1012-1014 kg. Snodgrass et al. (2006) provides the most recent values
for this comet's dimension and density. In
particular, with their time-series photometry they obtained a value for the
effective radius of the nucleus (Russel 1916) of
.
Even if accurate, this estimate is based on the assumption that the
geometrical albedo was equal to AR=0.04.
Furthermore, they derived a comet's minimum density equal to
.
Assuming thus a range of
possible densities (
)
and albedos
(
AR = 0.01-0.1) and using Eq. (1) in
Snodgrass et al. (2006) to derive the
corresponding effective radii, we obtained a total nuclear mass
between 1012 and 1014 kg. Given the uncertainty range in our mass estimate, we
concluded that the probable value of the expanding coma's mass resulting
from the outburst event ranged between 10-2 and 1 comet's mass.

There are different factors that could affect our results.
Dust grains in cometary ejecta typically span a range of
different dimensions and optical properties (see e.g. Lisse et al. 2007; Tozzi et al. 2007). Both the assumption on the uniform and homogeneous mass
distribution and the lack of specific observations able to constrain the dust
population characteristics for this particular object together justify our simplified
approach to summarizing the cloud's grain content, assuming a ``typical'' grain
dimension and the corresponding geometrical cross-section.
Another possible drawback in our coma's mass estimate
regards the pre-outburst activity of the comet.
During the most recent observations
of the comet obtained before the outburst (Snodgrass et al. 2006), the object
appeared to be inactive, although the heliocentric distance at that time
was 4.66 AU, whereas at the outburst it was 2.44 AU.
Moreover, it seems probable that the explosive event described in this
work largely overcame the common activity of the comet. Finally, the stars used
to probe the differential
extinction produced by the coma (Fig. 3), were
well-distributed inside the coma, avoiding the region close
to the comet's nucleus, and thus more closely reflecting the contribution to the
differential extinction of the material coming directly from the explosion.

Despite these approximations,
the result presented in Eq. (5),
has the advantage
to enlight the dependence
among the total mass of the cloud, the cloud's geometrical,
composition properties
and the observed differential extinctions, and of providing an estimate
for the expanding coma's mass that points towards a consistent
disintegration phenomenon, as suggested by
the large outburst event.

6 Conclusions

In this Letter we analyzed the early phases of the 2007 October 24 outburst
comet 17P/Holmes. We acquired BVRIphotometric images at the Wendelstein 0.8 m telescope
between October 26, 2007 and November 20, 2007. We observed a spherically
symmetric dust cloud moving
away from the comet nucleus with a mean projected constant velocity of
arcsec/day (
km s-1), while the
dust cloud was expanding with a mean constant velocity
of
arcsec/day (
km s-1).
These results agree with those
obtained during past outbursts of this comet.
Evidence of a gradient in the expansion velocity of the dust cloud was also
found with the velocity increasing towards the external regions. Finally,
performing differential photometry on background stars occulted
by the moving cloud, and assuming a uniform and homogeneous spherical
mass distribution, we derived a value of
1012-1014 kg for the coma's mass, around
10-2-1 of the comet's mass.
We interpreted our observations in the context of an explosive event,
probably caused by some internal instability processes rather than by an
asteroidal body's impact.
Various mechanisms have been proposed in the past
to explain the comets' splitting, involving tidal, thermal,
and rotational forces (Sekanina 1997). These processes could
have played an important role in the event discussed here,
although some specific characteristics allow us to consider it as more peculiar.
For example, the separation velocities of the splitting components
are generally a few ,
while in this case we found a projected
relative velocity around 2 orders of magnitude greater. The outburst itself
represents the largest apparent brightness increase ever observed for a comet.
In conclusion, we underline the importance of considering
other observational results in order to accurately characterize
this event and to provide a more insightful
view of its enigmatic and still not well-understood nature.

Acknowledgements

We warmly thank the anonymous Referee for the helpful comments and
suggestions allowing significant improvement to this Letter.